H-Infinity Stabilization for Singular Networked Cascade Control Systems With State Delay and Disturbance

This paper is concerned with the stabilization and H∞ control problems for a class of singular networked cascade control systems with state delay and disturbance. Via the fact that single loop feedback control shows a shortcoming in that the plant output as nonzero disturbance acts on the systems, a new model of singular networked cascade control system is proposed. In this system, both the network-induced delay and data packed dropout phenomena are considered. Based on the model, sufficient conditions are derived in terms of linear matrix inequalities and the corresponding H∞ stabilizing controller design technique is also developed based on the above conditions. The proposed method emphasizes the implementation issue and employs the cascade control to singular networked control systems. A simulation example is given to illustrate the proposed design procedures and its applications.

[1]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[2]  Dong Yue,et al.  State feedback controller design of networked control systems , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  G. Stépán.  Retarded dynamical systems : stability and characteristic functions , 1989 .

[4]  Fuchun Sun,et al.  Gain-Scheduling-Based State Feedback Integral Control for Networked Control Systems , 2011, IEEE Transactions on Industrial Electronics.

[5]  Mohamed Darouach,et al.  Novel bounded real lemma for discrete-time descriptor systems: Application to H∞ control design , 2012, Autom..

[6]  S. Niculescu,et al.  Stability analysis of time-delay systems : A lyapunov approach , 2006 .

[7]  Chunyu Yang,et al.  Exponential H ∞  filtering for singular systems with Markovian jump parameters , 2013 .

[8]  Rong-Jong Wai,et al.  Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism , 2008, IEEE Transactions on Fuzzy Systems.

[9]  R. G. Franks,et al.  Quantitative Analysis of Cascade Control , 1956 .

[10]  Yu Xia,et al.  Performance assessment of cascade control systems based on LQG benchmark , 2016, 2016 Chinese Control and Decision Conference (CCDC).

[11]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[12]  Françoise Lamnabhi-Lagarrigue,et al.  Cascade High Gain Predictors for a Class of Nonlinear Systems , 2012, IEEE Transactions on Automatic Control.

[13]  Nathan van de Wouw,et al.  Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance , 2010, IEEE Transactions on Automatic Control.

[14]  H. Akagi,et al.  Negative-sequence reactive-power control by a PWM STATCOM based on a modular multilevel cascade converter (MMCC-SDBC) , 2011, 2011 IEEE Energy Conversion Congress and Exposition.

[15]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[16]  Mohamed Yagoubi,et al.  On State Feedback $H_{\infty}$ Control for Discrete-Time Singular Systems. , 2013 .

[17]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[18]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[19]  Xiangjie Liu,et al.  H-Infinity State Feedback Control for a Class of Networked Cascade Control Systems With Uncertain Delay , 2010, IEEE Transactions on Industrial Informatics.

[20]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[21]  Mohamed Yagoubi,et al.  On State Feedback H∞ Control for Discrete-Time Singular Systems , 2013, IEEE Transactions on Automatic Control.

[22]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[23]  Daniel W. C. Ho,et al.  State/noise estimator for descriptor systems with application to sensor fault diagnosis , 2006, IEEE Transactions on Signal Processing.

[24]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[25]  Zhiguang Feng,et al.  Delay‐dependent robust H∞ controller synthesis for discrete singular delay systems , 2011 .

[26]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[27]  El Houssaine Tissir,et al.  Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays , 2013, Int. J. Autom. Comput..

[28]  Wilfrid Perruquetti,et al.  Observability and detectability of singular linear systems with unknown inputs , 2013, Autom..

[29]  Xun-lin Zhu,et al.  H∞ filtering for continuous‐time singular systems with time‐varying delay , 2011 .

[30]  Peng Shi,et al.  Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay , 2012, Int. J. Syst. Sci..

[31]  Fang Fang,et al.  Cascade control of superheated steam temperature with neuro-PID controller. , 2012, ISA transactions.

[32]  Xinli Li,et al.  Simulation for a class of networked cascade control systems by PID control , 2010, 2010 International Conference on Networking, Sensing and Control (ICNSC).

[33]  Qing Song,et al.  A Neural Network Assisted Cascade Control System for Air Handling Unit , 2007, IEEE Transactions on Industrial Electronics.

[34]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Discrete-Time Complex Networks With Randomly Occurring Sensor Saturations and Randomly Varying Sensor Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.